This figure is not drawn to scale. A rectangular glass container 72 cm by 55 cm by 49 cm has 2 compartments, E and F, with a water height of 32 cm in E and 20 cm in F. A hole in the slider caused water to leak from E to F. It was found that the water level in both compartments became the same after some time.
- What is the height of water in the container now?
- It took 134 h for the water in both compartments to reach the same level. Assuming that water leaked at a constant rate, how much water flowed from E to F in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment E
= 30 x 32 x 55
= 52800 cm
3 Length of Compartment F
= 72 - 30
= 42 cm
Volume of the water in Compartment F
= 42 x 55 x 20
= 46200 cm
3 Total volume of water
= 52800 + 46200
= 99000 cm
3 Base area of the glass container
= 72 x 55
= 3960 cm
2 Height of water
= 99000 ÷ 3960
= 25 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment E
= 32 - 25
= 7 cm
Drop in the volume of Compartment E
= 55 x 30 x 7
= 11550 cm
3 Volume of water flowed from E to F in 1 minute
= 11550 ÷ 105
≈ 110.0 cm
3 Answer(s): (a) 25 cm; (b) 110.0 cm
3